Decorrelation-Based Feature Discovery: GI-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 The Data

dataGI <- as.data.frame(read_excel("~/GitHub/LatentBiomarkers/Data/GI/data.xlsx", sheet = "Sheet1"))
dataGI$ID <- NULL

table(dataGI$V2)
#> 
#>  1  2 
#> 76 76
dataSet1 <- subset(dataGI,V2==1)
class <- dataSet1$V1
dataSet1$V1 <- NULL
dataSet1$V2 <- NULL
colnames(dataSet1) <- paste(colnames(dataSet1),"WL",sep="_")
dataSet2 <- subset(dataGI,V2==2)
dataSet2$V1 <- NULL
dataSet2$V2 <- NULL
colnames(dataSet2) <- paste(colnames(dataSet2),"NBI",sep="_")
dataGI <- cbind(dataSet1,dataSet2)
dataGI$class <- 1*(class > 1)
table(dataGI$class)
#> 
#>  0  1 
#> 21 55

1.2.0.1 Standarize the names for the reporting

studyName <- "GI"
dataframe <- dataGI
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
76	1396

pander::pander(table(dataframe[,outcome]))

0	1
21	55

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9999797

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  V644_WL V599_WL V497_NBI V497_WL V49_NBI V443_WL 
#>     V3_WL     V4_WL     V5_WL     V6_WL     V7_WL     V8_WL 
#> 0.7462069 0.6082759 0.5172414 0.5158621 0.5365517 0.5310345 
#> 
#>  Included: 725 , Uni p: 0.0002068966 , Base Size: 6 , Rcrit: 0.3949911 
#> 
#> 
 1 <R=0.942,thr=0.950>, Top: 69< 48 >[Fa= 69 ]( 69 , 178 , 0 ),<|><>Tot Used: 247 , Added: 178 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=0.919,thr=0.950>, Top: 15< 25 >[Fa= 84 ]( 15 , 88 , 69 ),<|><>Tot Used: 308 , Added: 88 , Zero Std: 0 , Max Cor: 0.999
#> 
 3 <R=0.910,thr=0.950>, Top: 12< 5 >[Fa= 94 ]( 10 , 40 , 84 ),<|><>Tot Used: 318 , Added: 40 , Zero Std: 0 , Max Cor: 0.989
#> 
 4 <R=0.903,thr=0.950>, Top: 4< 2 >[Fa= 98 ]( 4 , 7 , 94 ),<|><>Tot Used: 321 , Added: 7 , Zero Std: 0 , Max Cor: 0.950
#> 
 5 <R=0.901,thr=0.900>, Top: 92< 1 >[Fa= 147 ]( 88 , 148 , 98 ),<|><>Tot Used: 469 , Added: 148 , Zero Std: 0 , Max Cor: 0.949
#> 
 6 <R=0.866,thr=0.900>, Top: 16< 1 >[Fa= 154 ]( 16 , 17 , 147 ),<|><>Tot Used: 487 , Added: 17 , Zero Std: 0 , Max Cor: 0.907
#> 
 7 <R=0.860,thr=0.900>, Top: 1< 1 >[Fa= 155 ]( 1 , 1 , 154 ),<|><>Tot Used: 489 , Added: 1 , Zero Std: 0 , Max Cor: 0.900
#> 
 8 <R=0.860,thr=0.800>, Top: 98< 2 >[Fa= 195 ]( 92 , 152 , 155 ),<|><>Tot Used: 573 , Added: 152 , Zero Std: 0 , Max Cor: 0.926
#> 
 9 <R=0.855,thr=0.900>, Top: 2< 1 >[Fa= 196 ]( 2 , 2 , 195 ),<|><>Tot Used: 574 , Added: 2 , Zero Std: 0 , Max Cor: 0.897
#> 
 10 <R=0.852,thr=0.800>, Top: 29< 1 >[Fa= 205 ]( 26 , 38 , 196 ),<|><>Tot Used: 601 , Added: 38 , Zero Std: 0 , Max Cor: 0.894
#> 
 11 <R=0.849,thr=0.800>, Top: 8< 2 >[Fa= 210 ]( 7 , 11 , 205 ),<|><>Tot Used: 613 , Added: 11 , Zero Std: 0 , Max Cor: 0.884
#> 
 12 <R=0.857,thr=0.800>, Top: 5< 1 >[Fa= 213 ]( 4 , 5 , 210 ),<|><>Tot Used: 620 , Added: 5 , Zero Std: 0 , Max Cor: 0.884
#> 
 13 <R=0.884,thr=0.800>, Top: 1< 1 >[Fa= 213 ]( 1 , 1 , 213 ),<|><>Tot Used: 620 , Added: 1 , Zero Std: 0 , Max Cor: 0.884
#> 
 14 <R=0.864,thr=0.800>, Top: 2< 1 >[Fa= 213 ]( 1 , 1 , 213 ),<|><>Tot Used: 620 , Added: 1 , Zero Std: 0 , Max Cor: 0.881
#> 
 15 <R=0.881,thr=0.800>, Top: 1< 1 >[Fa= 213 ]( 1 , 1 , 213 ),<|><>Tot Used: 620 , Added: 1 , Zero Std: 0 , Max Cor: 0.868
#> 
 16 <R=0.847,thr=0.800>, Top: 2< 1 >[Fa= 213 ]( 1 , 1 , 213 ),<|><>Tot Used: 620 , Added: 1 , Zero Std: 0 , Max Cor: 0.814
#> 
 17 <R=0.814,thr=0.800>, Top: 1< 1 >[Fa= 213 ]( 1 , 1 , 213 ),<|><>Tot Used: 620 , Added: 1 , Zero Std: 0 , Max Cor: 0.799
#> 
 18 <R=0.799,thr=0.800>
#> 
 [ 18 ], 0.7993308 Decor Dimension: 620 Nused: 620 . Cor to Base: 369 , ABase: 725 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

7.73e+08

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

1.55e+08

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

0.306

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.217

varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))

La_V698_WL	La_V699_WL	La_V677_WL	La_V681_WL	La_V692_WL	La_V468_NBI
4.59e-05	4.01e-05	3.78e-05	3.72e-05	3.61e-05	1.73e-06

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

1.5.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 620

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 161

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

[1] 130

    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
#      fc <- cluster_optimal(gr)
        fc <- cluster_walktrap (gr,steps=50)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }

pander::pander(clustable)

	Formula	Class	ResidualVariance	Fscore
V625_WL	+ V625_WL - (6.880)V639_WL + (6.292)V644_WL	1	0.018	8
V620_WL	+ V620_WL - (1.557)V622_WL + (0.546)V625_WL	1	0.006	3
V622_WL	+ V622_WL - (1.121)V625_WL	1	0.007	1
V616_WL	+ V616_WL - (2.130)V620_WL + (1.148)V625_WL	1	0.006	-1
V623_WL	+ V623_WL - (1.070)V625_WL	1	0.003	-1
V624_WL	+ V624_WL - (1.032)V625_WL	1	0.001	-1
V649_WL	- (0.862)V644_WL + V649_WL	2	0.005	2
V675_WL	+ (0.886)V644_WL - (0.027)V649_WL - (1.624)V652_WL + V675_WL	3	0.004	22
V682_WL	+ (0.232)V675_WL - (1.188)V679_WL + V682_WL	3	0.001	17
V691_WL	+ (0.706)V675_WL - (1.647)V682_WL + V691_WL	3	0.000	4
V679_WL	- (0.906)V675_WL + V679_WL	3	0.002	2
V696_WL	+ (0.943)V675_WL - (1.842)V682_WL + V696_WL	3	0.001	1
V676_WL	- (0.974)V675_WL + V676_WL	3	0.001	0
V695_WL	+ (0.292)V675_WL - (0.405)V682_WL - (0.841)V691_WL + V695_WL	3	0.000	-1
V683_WL	+ (0.025)V675_WL - (1.005)V682_WL + V683_WL	3	0.000	-1
V687_WL	+ (0.374)V675_WL - (1.331)V682_WL + V687_WL	3	0.000	-1
V198_NBI	NA	4	1.000	18
V184_NBI	+ V184_NBI - (48.677)V198_NBI	4	0.346	4
V232_WL	+ V232_WL - (17.711)V198_NBI	4	0.339	2
V180_NBI	+ V180_NBI - (0.850)V198_NBI	4	0.195	2
V216_NBI	- (1.054)V198_NBI + V216_NBI	4	0.113	1
V224_NBI	- (1.084)V198_NBI + V224_NBI	4	0.092	1
V188_NBI	+ V188_NBI - (1.022)V198_NBI	4	0.064	0
V228_NBI	- (4.83e-03)V198_NBI - (1.013)V224_NBI + V228_NBI	4	0.012	0
V296_NBI	- (13.104)V198_NBI + V296_NBI	4	0.192	0
V639_WL	+ V639_WL - (1.186)V644_WL	5	0.006	4
V644_WL	NA	6	1.000	50
V652_WL	+ (0.313)V644_WL - (1.276)V649_WL + V652_WL	6	0.002	23
V662_WL	+ (0.570)V644_WL - (1.474)V652_WL + V662_WL	6	0.002	3
V667_WL	+ (0.350)V644_WL - (0.624)V652_WL - (0.628)V662_WL + V667_WL	6	0.001	2
V658_WL	+ (0.417)V644_WL - (1.370)V652_WL + V658_WL	6	0.002	2
V642_WL	+ V642_WL - (1.076)V644_WL	6	0.001	0
V646_WL	- (0.944)V644_WL + V646_WL	6	0.001	0
V673_WL	- (0.059)V644_WL + (0.366)V652_WL - (1.304)V667_WL + V673_WL	6	0.000	-1
V643_WL	+ V643_WL - (1.033)V644_WL	6	0.001	-1
V645_WL	- (0.978)V644_WL + V645_WL	6	0.000	-1
V653_WL	+ (0.059)V644_WL - (1.048)V652_WL + V653_WL	6	0.000	-1
V228_WL	- (1.150)V192_WL + V228_WL	7	0.171	12
V182_WL	+ V182_WL - (0.687)V228_WL	7	0.086	1
V194_WL	+ V194_WL - (0.843)V228_WL	7	0.038	0
V208_WL	+ V208_WL - (1.128)V228_WL	7	0.046	0
V216_WL	+ V216_WL - (0.812)V228_WL	7	0.062	0
V172_WL	+ V172_WL - (7.270)V228_WL	7	0.088	-1
V196_WL	+ V196_WL - (0.982)V228_WL	7	0.044	-1
V220_WL	+ V220_WL - (0.440)V228_WL	7	0.063	-1
V224_WL	+ V224_WL - (0.983)V228_WL	7	0.013	-1
V288_WL	- (0.452)V228_WL + V288_WL	7	0.069	-1
V424_WL	- (81.331)V208_WL + (91.739)V228_WL + V424_WL	7	0.296	-1
V635_WL	+ V635_WL - (1.913)V639_WL + (0.915)V644_WL	8	0.003	8
V630_WL	+ V630_WL - (1.924)V635_WL + (1.027)V644_WL	8	0.003	1

par(op)

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9419448

1.8 U-MAP Visualization of features

1.8.1 The UMAP on Raw Data

  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

V172_WL, V474_NBI, V477_NBI, V220_WL, V220_NBI and V470_NBI

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

1.8.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

V474_NBI, V169_WL, V492_NBI, V499_NBI, V280_NBI and V499_WL

  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : V102_WL 200 : V288_WL 300 : V535_WL 400 : V635_WL 500 : V37_NBI
600 : V137_NBI 700 : V470_NBI

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_V102_WL 200 : La_V288_WL 300 : La_V535_WL 400 : La_V635_WL 500 : V37_NBI
600 : La_V137_NBI 700 : La_V470_NBI

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
V172_WL	3.55e+03	1.78e+03	1046.667	537.2409	0.718095	0.933
V220_NBI	2.01e+02	1.20e+02	51.524	27.8220	0.747592	0.929
V220_WL	1.96e+02	1.07e+02	52.381	42.7370	0.097268	0.927
V477_NBI	6.18e-02	2.98e-02	0.149	0.1717	0.000358	0.925
V169_NBI	1.26e+03	8.24e+02	346.619	198.5476	0.350000	0.920
V196_NBI	4.52e+02	2.51e+02	134.238	66.3226	0.410564	0.920
V182_NBI	3.44e+02	2.17e+02	95.190	48.8412	0.793090	0.915
V470_NBI	3.79e-01	1.34e-01	0.188	0.0682	0.948083	0.913
V182_WL	3.17e+02	1.69e+02	96.476	87.3691	0.142781	0.912
V474_NBI	3.40e+00	3.13e-01	2.680	0.5481	0.222068	0.912

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
V474_NBI	3.40e+00	3.13e-01	2.68e+00	5.48e-01	0.2221	0.912
V492_NBI	4.74e-01	1.31e-01	2.68e-01	8.02e-02	0.6487	0.908
V169_WL	1.20e+03	6.66e+02	4.03e+02	4.20e+02	0.0543	0.897
V474_WL	3.19e+00	4.57e-01	2.36e+00	5.29e-01	0.9972	0.882
V499_NBI	7.46e-02	2.83e-02	1.34e-01	4.82e-02	0.8421	0.873
La_V69_WL	1.03e-03	1.66e-03	-1.02e-03	1.56e-03	0.3074	0.872
V280_NBI	4.18e+02	3.20e+02	1.37e+02	7.23e+01	0.4410	0.870
V473_NBI	1.22e-01	4.19e-02	2.12e-01	1.67e-01	0.0188	0.865
V499_WL	1.04e-01	4.95e-02	1.99e-01	8.56e-02	0.6162	0.858
V480_WL	3.86e+01	1.15e+01	2.41e+01	7.91e+00	0.4542	0.855
La_V200_NBI	-1.08e+03	2.09e+03	1.03e+03	2.22e+03	0.0393	0.835
La_V500_WL	9.13e-01	2.66e-02	9.49e-01	2.80e-02	0.8294	0.833
La_V27_NBI	9.48e-04	5.84e-04	1.73e-03	5.82e-04	0.9547	0.831
La_V260_NBI	-3.87e+01	3.91e+01	-1.46e+01	1.30e+01	0.3994	0.820

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.36	527	0.722

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores	varratio
V172_WL	NA	3.55e+03	1.78e+03	1.05e+03	5.37e+02	0.718095	0.933	0.933	NA	NA
V220_NBI	NA	2.01e+02	1.20e+02	5.15e+01	2.78e+01	0.747592	0.929	0.929	NA	NA
V220_WL	NA	1.96e+02	1.07e+02	5.24e+01	4.27e+01	0.097268	0.927	0.927	NA	NA
V477_NBI	NA	6.18e-02	2.98e-02	1.49e-01	1.72e-01	0.000358	0.925	0.925	NA	NA
V169_NBI	NA	1.26e+03	8.24e+02	3.47e+02	1.99e+02	0.350000	0.920	0.920	NA	NA
V196_NBI	NA	4.52e+02	2.51e+02	1.34e+02	6.63e+01	0.410564	0.920	0.920	NA	NA
V182_NBI	NA	3.44e+02	2.17e+02	9.52e+01	4.88e+01	0.793090	0.915	0.915	NA	NA
V470_NBI	NA	3.79e-01	1.34e-01	1.88e-01	6.82e-02	0.948083	0.913	0.913	NA	NA
V474_NBI	NA	3.40e+00	3.13e-01	2.68e+00	5.48e-01	0.222068	0.912	0.912	0	1.0000
V182_WL	NA	3.17e+02	1.69e+02	9.65e+01	8.74e+01	0.142781	0.912	0.912	NA	NA
V492_NBI	NA	4.74e-01	1.31e-01	2.68e-01	8.02e-02	0.648736	0.908	0.908	2	1.0000
V169_WL	NA	1.20e+03	6.66e+02	4.03e+02	4.20e+02	0.054330	0.897	0.897	5	1.0000
V474_WL	NA	3.19e+00	4.57e-01	2.36e+00	5.29e-01	0.997159	0.882	0.882	0	1.0000
V499_NBI	NA	7.46e-02	2.83e-02	1.34e-01	4.82e-02	0.842141	0.873	0.873	1	1.0000
La_V69_WL	- (1.863)V47_WL + V69_WL	1.03e-03	1.66e-03	-1.02e-03	1.56e-03	0.307376	0.872	0.617	0	0.1015
V280_NBI	NA	4.18e+02	3.20e+02	1.37e+02	7.23e+01	0.441009	0.870	0.870	6	1.0000
V473_NBI	NA	1.22e-01	4.19e-02	2.12e-01	1.67e-01	0.018789	0.865	0.865	2	1.0000
V499_WL	NA	1.04e-01	4.95e-02	1.99e-01	8.56e-02	0.616245	0.858	0.858	5	1.0000
V480_WL	NA	3.86e+01	1.15e+01	2.41e+01	7.91e+00	0.454234	0.855	0.855	5	1.0000
La_V200_NBI	- (0.862)V184_NBI + V200_NBI	-1.08e+03	2.09e+03	1.03e+03	2.22e+03	0.039308	0.835	0.763	-1	0.0406
La_V500_WL	+ (0.127)V497_WL + V500_WL	9.13e-01	2.66e-02	9.49e-01	2.80e-02	0.829410	0.833	0.797	1	0.2510
La_V27_NBI	+ V27_NBI - (0.464)V49_NBI	9.48e-04	5.84e-04	1.73e-03	5.82e-04	0.954721	0.831	0.588	-1	0.1221
La_V260_NBI	+ V260_NBI - (0.177)V280_NBI	-3.87e+01	3.91e+01	-1.46e+01	1.30e+01	0.399448	0.820	0.817	1	0.3079

1.10 Comparing ILAA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	17	4
1	3	52

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.908	0.819	0.962
3	se	0.945	0.849	0.989
4	sp	0.810	0.581	0.946
6	diag.or	73.667	14.963	362.674

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	17	4
1	0	55

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.947	0.871	0.985
3	se	1.000	0.935	1.000
4	sp	0.810	0.581	0.946
6	diag.or	Inf	NA	Inf

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	15	6
1	2	53

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.895	0.803	0.953
3	se	0.964	0.875	0.996
4	sp	0.714	0.478	0.887
6	diag.or	66.250	12.104	362.601

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	11	10
1	0	55

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.868	0.771	0.935
3	se	1.000	0.935	1.000
4	sp	0.524	0.298	0.743
6	diag.or	Inf	NA	Inf

  par(op)